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| -rw-r--r-- | hidden_order.bib | 10 | ||||
| -rw-r--r-- | main.tex | 4 | ||||
| -rw-r--r-- | ref_response.tex | 20 |
3 files changed, 22 insertions, 12 deletions
diff --git a/hidden_order.bib b/hidden_order.bib index 2e0de7c..57ae872 100644 --- a/hidden_order.bib +++ b/hidden_order.bib @@ -679,3 +679,13 @@ } +@article{yanagisawa2012gamma3, + title={$\Gamma$3-type lattice instability and the hidden order of URu2Si2}, + author={Yanagisawa, Tatsuya and Mombetsu, Shota and Hidaka, Hiroyuki and Amitsuka, Hiroshi and Akatsu, Mitsuhiro and Yasin, Shadi and Zherlitsyn, Sergei and Wosnitza, Jochen and Huang, Kevin and Brian Maple, M}, + journal={Journal of the Physical Society of Japan}, + volume={82}, + number={1}, + pages={013601}, + year={2012}, + publisher={The Physical Society of Japan} +}
\ No newline at end of file @@ -140,11 +140,11 @@ under pressure.\cite{Choi_2018} Above 0.13--0.5 $\GPa$ (depending on temperature), \urusi\ undergoes a $\Bog$ nematic distortion, which might be related to the anomalous softening of the $\Bog$ elastic modulus $(C_{11}-C_{12})/2$ that occurs over a broad temperature range at zero -pressure.\cite{Wolf_1994, Kuwahara_1997} Motivated by these results---which +pressure.\cite{Wolf_1994, Kuwahara_1997,yanagisawa2012gamma3} Motivated by these results---which hint at a $\Bog$ strain susceptibility associated with the \ho\ state---we construct a phenomenological mean field theory for an arbitrary \op\ coupled to strain, and then determine the effect of its phase transitions on the elastic -response in different symmetry channels. +response in different symmetry channels. We find that only one \op\ representation reproduces the anomalous $\Bog$ elastic modulus, which softens in a Curie--Weiss-like manner from room diff --git a/ref_response.tex b/ref_response.tex index 78524bc..0f4c7a9 100644 --- a/ref_response.tex +++ b/ref_response.tex @@ -190,8 +190,8 @@ in the context of interpreting ultrasound data does appear to be somewhat novel. There are a couple of very important distinctions to be made between our work and the work of ref. 25 (K. Kuwahara et al.), which as the referee points out, also identified softening in $(c_{11}-c_{12})/2$. First, the data in ref.\ 25 -(figure 2c) appear to be contaminated by the c66 mode, based on the fact that -the peak in c66 appears around 60 K. In the work of T. Yanagisawa et al +(figure 2c) appear to be contaminated by the $c_{66}$ mode, based on the fact that +the peak in $(c_{11}-c_{12})/2$ appears around 60 K. In the work of T. Yanagisawa et al (Journal of the Physical Society of Japan 82 (2013) 013601), the peak is at 130 K, and the elastic constant softens back down to its room-temperature value by $T_{HO}$. The data we show in figure 2b, obtained with resonant ultrasound, @@ -200,15 +200,15 @@ value by $T_{HO}$. The contamination in ref.\ 25 is likely an artifact of the pulse-echo ultrasound technique, which can mix between $c_{66}$ and $(c_{11}-c_{12})/2$ when the crystal is not perfectly aligned. -Perhaps more -importantly, the fit shown in figure 4 of ref 25 does not show very good +Second, and more +critically, the fit shown in figure 4 of ref. 25 does not show very good agreement with the data at any temperature. The model used is one for -thermally-populated crystal field levels, and does not directly relate to the phase +thermally-populated crystal field levels, and it does not directly relate to the phase transition at $T_{HO}$. This model does not produce the sharp change in slope of $(c_{11}-c_{12})/2$ at $T_{HO}$, which is an essential singularity in the -thermodynamic free energy and must appear in the elastic moduli at a second order phase transition, and it does -not produce $1/(T-T_0)$ strain susceptibility above $T_{HO}$, which is a -signature of strain and order parameter coupling. To summarize, while ref. 25 does indeed propose a model to describe the softening seen in $(c_{11}-c_{12})/2$, it does not attribute the softening to the presence of an order parameter, does not capture the singularity at the phase transition, and does not provide a good match to the Curie-Weiss behaviour of the elastic constant. \\ +thermodynamic free energy and which must appear in the elastic moduli at a second order phase transition. The crystal field model does attempt to reproduce the termination of the softening below $T_{HO}$, but it does so only in a smooth way, with no discontinuity in slope at $T_{HO}$. + +To summarize, while ref. 25 does indeed propose a model to describe the softening seen in $(c_{11}-c_{12})/2$, the data in ref. 25 are contaminated by $c_{66}$, the model does not attribute the softening to the presence of an order parameter, it does not capture the singularity at the phase transition, and does not provide a good match to the Curie-Weiss behaviour of the elastic constant above $T_{HO}$. Whether or not the approach of ref. 25 is correct, it is entirely distinct from the approach we have taken here. \\ {\color{blue} 3) The agreement of C[B1g] in the region $T<T_{HO}$ is poor, though only @@ -241,7 +241,7 @@ transition. Thus a B$_{\rm{1g}}$ order parameter is indeed unique in capturing b most relevant in this problem. }\\ -We agree that the presence of a super-lattice structure is still a debated point, but there are many other experiments that give evidence for the formation of a superlattice structure along the c-axis at ambient pressure, e.g.:\\ +We agree that this is still a point under debate in the community, but there are many other experiments that give evidence for the formation of a superlattice structure along the c-axis at ambient pressure, e.g.:\\ C.\ Bareille, F.\ L.\ Boariu, H.\ Schwab, P.\ Lejay, F.\ Reinert, and A.\ F. Santander-Syro, Nature Communications \textbf{5}, 4326 (2014). @@ -258,6 +258,6 @@ J.-Q.\ Meng, P.\ M.\ Oppeneer, J.\ A.\ Mydosh, P.\ S.\ Riseborough, K.\ Gofryk, Joyce, E.\ D.\ Bauer, Y.\ Li, and T.\ Durakiewicz, Physical Review Letters \textbf{111}, 127002 (2013).\\ -While the ultrasound experiment cannot determine the precise wavevector, the most natural way to get Curie-Weiss susceptibility in the B$_{\rm{1g}}$ elastic modulus that is cut off (instead of falling all the way to zer) at $T_{\rm{HO}}$ is to have a B$_{\rm{1g}}$ order parameter modulated at a finite wavevector, pushing the divergent susceptibility out to finite $q$ where it is unobserved (or not fully-observed) by the $q=0$ ultrasound. +While the ultrasound experiment cannot directly determine the wavevector, the most natural way to get Curie-Weiss susceptibility in the B$_{\rm{1g}}$ elastic modulus that is cut off (instead of falling all the way to zero) at $T_{\rm{HO}}$ is to have a B$_{\rm{1g}}$ order parameter modulated at a finite wavevector. This pushes the divergent susceptibility out to finite $q$ where it is unobserved (or not fully-observed) by the $q=0$ ultrasound. \end{document} |